A Hybrid Solver Based on Efficient BEM-Potential and LBM-NS Models: Recent BEM Developments and Applications to Naval Hydrodynamics

Mivehchi, Amin (University of Rhode Island) | Harris, Jeffrey C. (University of Paris-Est) | Grilli, Stephan T. (University of Rhode Island) | Dahl, Jason M. (University of Rhode Island) | O'Reilly, Chris M. (University of Rhode Island, Navatek Ltd.) | Kuznetsov, Konstantin (University of Paris-Est) | Janssen, Christian F. (Hamburg University of Technology (TUHH))



We report on recent developments of a 3D hybrid model for naval hydrodynamics based on a perturbation method, in which velocity and pressure are decomposed as the sum of an inviscid flow and a viscous perturbation. The far- to near-field inviscid flows are solved with a Boundary Element Method (BEM), based on fully nonlinear potential flow theory, accelerated with a fast multipole method (FMM), and the near-field perturbation flow is solved with a Navier-Stokes (NS) model based on a Lattice Boltzmann Method (LBM) with a LES modeling of turbulent properties. The BEM model is efficiently parallelized on CPU clusters and the LBM model on massively parallel GPGPU co-processors.

The hybrid model formulation and its latest developments and implementation, in particular, regarding the improvement and validation of the model for naval hydrodynamics applications, are presented in a companion paper by O'Reilly et. al (2017), in this conference. In this paper, we concentrate on the BEM model aspects and show that the BEM-FMM can accurately solve a variety of problems while providing a nearly linear scaling with the number of unknowns (up to millions of nodes) and a speed-up with the number of processors of 35-50%, for small (e.g., 24 cores) to large (e.g., hundreds of cores) CPU clusters.


The simulation of the dynamic response of maritime structures in waves and wave-induced forces is typically based on linear wave models, such as AEGIR (Kring et al.,1999), or in case of large motions and/or steep waves, on using nonlinear wave models based on potential flow theory (PFT), usually solved with a higher-order Boundary element method (BEM). For structures with a forward speed, semi-empirical corrections are often made to account for viscous/turbulent effects in the total resistance. While standard Computational Fluid Dynamics (CFD) models based on the full Navier-Stokes (NS) equations can also be used to simulate such problems, their computational cost is typically too prohibitive and their accuracy for long-term wave modeling usually less than that of PFT-BEM models. However, in some cases, the viscous/turbulent flow around the structure's hull and possible breaking waves and wakes require to be more accurately modeled to capture the salient physics of the problem.